时变非线性分布参数控制系统的小波辨识算法

IDENTIFICATION ALGORITHM OF TIME-VARYING NON-LINEAR DISTRIBUTED PARAMETER SYSTEMS BASED ON WAVELETS

基于正交函数逼近理论,在Haar小波正交规范基的基础上,总结并推导出了其积分运算矩阵、微分运算矩阵、乘积运算矩阵及其运算性质,并应用于一类时变非线性分布参数系统的辨识。借助于正交小波函数逼近方法对分布参数系统进行辨识,经正交小波逼近变换转化为代数矩阵方程,因此该方法可以不考虑初始条件和边界条件,较其他辨识方法要简单得多。该算法简单、计算量小、简化了分布参数系统辨识的求解过程,应用在分布参数系统辨识中不失为一种有效的分析方法。

In this paper, the orthogonal function approximation theory is applied to dealing with the identification problem of a class of time- varying non-linear distributed parameter systems, and Haar wavelets have been chosen as orthogonal functions. Based on Haar orthogonal wavelets function basis, some operational matrices of Haar wavelet are summarized and derived ,they are forward integral operational matrix, differential operational matrix and element product operational matrix. Moreover, some operational properties of wavelet transformation are obtained. And the orthogonal wavelets function approximation method has been applied to the identification of distributed parameter systems. Because of the application, the time-varying non-linear distributed parameter system described by PDEs has been transformed into an algebraic matrix equation problem. In particular, because initial conditions and boundary conditions mustn＇t be taken into account, the proposed method is much simpler than others. It is illustrated that this method has advantages of simple algorithm, less computation, simplifies the process of solution. The presented method is an efficient analysis approach for the parameters identification on its application to time-varying non-linear distributed parameter systems.